Elliptic de Sitter space:dS/Z2

Abstract

We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an "elliptic" Z 2 -identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analog of an S-matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter-invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite-dimensional and still have positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.

The black hole S-Matrix from quantum mechanics

“…However, owing to the validity of the S-Matrix only in the region of space-time that is near the horizon, this identification is presumably valid only in this region. Global identifications of the two exteriors have been considered in the past [60][61][62]. The physics of the scattering, with this identification is now clear.…”

Mach’s holographic principle

“…Unlike the black hole membrane paradigm, for which only those observers who remain outside the black hole see a membrane, here every observer has its own stretched horizon. The physical interpretation of the membrane in such a scenario probably involves some form of observer complementarity [28].…”

“…These gravity waves travel on null trajectories with respect to the background metric. Now, if a gravity wave intersects the timelike boundary, its amplitude and derivatives leave a corresponding perturbation on the boundary matter, via (6) and (7), and then (24) and (28).…”

Foliation-dependence of CFTs in Lorentzian-AdS/CFT

“…Yet their dual versions, bulk-Bob and bulk-Alice, have a nonzero amplitude to interact in the shared future region. While this may perhaps be possible if we consider a Z 2 identification [42], with excitations also respecting the same identification, it seems hard to understand for the usual eternal BTZ black hole. Conceptual puzzles related to this issue have been raised in [18][19][20] and other puzzles with this picture have been raised in [16].…”